In general, those modifiers help keep you focused on the things that you cannot start or do until that date.

Here's the full explanation from the Toodledo Help pages.

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How can I hide tasks that are due in the future?

Sometimes a task can only be completed on a specific due date (like a dentist appointment) and being reminded about it ahead of time is unnecessary. You can fix this by putting an = sign before the date. For example "=2008-01-01". This signifies that this task can only be completed on Jan 1, 2008 and that we shouldn't worry about it until then.

Sometimes a task cannot be completed until after a specific duedate. You can place a ">" sign before the date to tell Toodledo the earliest date that this task can be completed. For example ">2008-01-01" means that this task cannot be completed until Jan 1, 2008 has passed. Toodledo will know not to bug you about this task until the specified date arrives.

You can also designate a task as optional by placing a "?" in front of the due date. This acts like "=", but if the date passes and you have not completed the task, the task will be automatically removed, or moved forward if it is a repeating task.

Tasks that use a due-date modifier will not show up on your hotlist until they are due (unless they have a high enough priority). If you use a due-date modifier and the task is more than 1 week in the future, it will also be hidden from your other lists unless you turn on the "Show Due in the Future" filter. The exception is that even if you use a due-date modifier, tasks will not be hidden when in the "Due-Date" view, or when using the "Search" view to find future tasks.

If you want to hide future tasks, without using a due-date modifier, you can go into your account settings and edit the settings under "Hide Future Tasks".

Additionally, you can use the start date field to hide tasks that occur in the future.

Thank you for clarifying = and > usage. I still have a problem/question.

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I realize when on the web site, tasks will show on screen out 1 week even if we hide future tasks. Can using = and > change that to hide some tasks?

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Printed booklet display (most important for me)

I am using = and > with the desire to have them not print until that day. But tasks with = and > are still displaying on my printed booklet when I show a folder or context on a page.

For example, I have a context of "out" for errands to run while out of the house. I would like to get the printed booklet to just show tasks I need to think about right now. But on the printed booklet the "out" context shows tasks even if they have a =date over a month from now.
Interestingly, one task for MANY months from now does NOT show.

Is it possible to get the printed booklet to just show tasks I need to think about right now?
Am I missing something or doing something wrong?

just to add my voice to the choir, i'd really like the booklet to honor "=" and ">", and also not to print items with start or due dates that are, say, 14 or more days in the future. my booklet always prints my annual january 1st recurring items, which aren't useful to me here in august.

No, you are not missing anything. The booklet currently does not obey the = and > flags. We hope to get this fixed soon.

is there any news on this? my booklet is still printed each time with items scheduled for six months from now, and i have to go through and scratch such things off before i can see what's actually useful on the lists.

The exception is that even if you use a due-date modifier, tasks will not be hidden when in the "Due-Date" view, or when using the "Search" view to find future tasks.

Is there any way to set up the search view to do this as well, or is there a way to emulate it with the search? I have a bunch of contexts and sometimes multiple of them are active at once (personal & web, work & web) so I setup searches for them, but having these tasks which are more than a month away sometimes show up in the search is bad because they show up higher than all the other things, even without a due date.